PSI - Issue 5

Paul Judt et al. / Procedia Structural Integrity 5 (2017) 769–776 Judt et. al. / Structural Integrity Procedia 00 (2017) 000 – 000

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1. Introduction

In the past, crack paths in composite materials such as in laminates, particle or fiber reinforced composites were studied e.g. by Keck and Fulland (2016), Borstnar et. al. (2016), Patrício and Mattheij (2010), Tilbrook et. al. (2005) and Wulf et. al. (1996). The difficulty of predicting the crack paths in such materials is related to the interplay of different energy consuming processes during fracture. On the one hand, the potential energy is reduced due to crack growth in the constituents of the composite. On the other, the delamination of interfaces between matrix and particles plays a crucial role with respect to the global energy release rate and the evolution of matrix cracks. Typically, the theory of linear elastic fracture mechanics (LEFM) is adapted to formulate the crack tip stress and displacement fields and the crack tip loading quantities in a crack growth simulation. In the case of composite materials, non-linear effects of interface delamination provide an elastic-plastic material behavior on the global level and thus theoretically must be considered in the simulation. Adding a coupling agent to the bulk material leads to an embrittlement of the composite and therefore small scale yielding (SSY) conditions can be assumed. Under SSY conditions the loading quantities of LEFM, such as stress intensity factors (SIF), energy release rate (ERR) or the J -integral (Rice, 1968) provide valid measures for the crack driving force or the crack deflection angle. In the following, FE-simulations in connection with a remeshing procedure with intelligent mesh refinement at the crack is applied to model crack growth. The crack driving force is calculated from the J k -integral in connection with some special numerical treatment in the vicinity of the crack tip, where the numerical data are inaccurate (Judt and Ricoeur, 2013). Applying this approach to cracks in aluminum alloy specimens with anisotropic fracture toughness provides numerical crack paths that are in very good agreement with experiments (Judt et. al., 2015a). To accurately predict the paths, details about the fracture toughness anisotropy are necessary, which are obtained from e.g. CT-tests. In aluminum alloys the fracture toughness anisotropy is related to the texture of the microstructure. Zarges et. al. (2017) and Judt et. al. (2017) investigated the anisotropy of the crack resistance in short fiber reinforced PP composites, which are related to the orientation of the crack ligament with respect to the predominant fiber orientation. The authors investigated crack paths in initially mode-I loaded CT-specimens with different predominant directions and observed an immediate crack deflection in certain specimen configurations. This phenomenon was also observed by Keck and Fulland (2016) and is related to the fracture toughness anisotropy. In this paper the effects of a small plastic zone in front of the crack tip are investigated, regarding the absolute value of the loading quantity and the crack deflection angle. Furthermore, the experimental crack paths in composites with a coupling agent are compared to calculated paths.

Nomenclature a

crack length

A b

surface

specimen thickness

d p G J c c J

expansion of the plastic zone along the ligament

energy release rate crack resistance

PD

crack resistance for crack growth parallel to the predominant direction TD c J crack resistance for crack growth transverse to the predominant direction J k J -integral vector K I mode-I stress intensity factor K II mode-II stress intensity factor n j normal vector Q kj energy-momentum tensor R radius of a circular integration contour 0  t expansion of the plastic wake perpendicular to the crack faces u strain energy density u e contribution of the elastic strains to the stress work density u i displacement vector